Ambient metric construction of CR invariant differential operators

Ambient constructions for Sasakian $η$-Einstein manifolds

The theory of ambient spaces is useful to define CR invariant objects, such as CR invariant powers of the sub-Laplacian, the $P$-prime operators, and $Q$-prime curvature. However in general, it is difficult to write down these objects in terms of the Tanaka-Webster connection. In this paper, we give those explicit formulas for CR manifolds satisfying an Einstein condition, called Sasakian $η$-Einstein manifolds. As an application, we study properties of the first and the second variation of the total $Q$-prime curvature at Sasakian $η$-Einstein manifolds.

度量Arnold余秩问题的证明

Proof of the metric Arnold's corank problem

本文证明了复超曲面中乘积为二的余秩是ambient bi-Lipschitz不变量，并解决了度量Arnold余秩问题。